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We consider the problem of determining a vector \(x \in {\mathbb R}^{n\times n}\) with \(A \, x = b\) for an invertible matrix \(A \in {\mathbb R}^{n\times n}\) and a vector \(b \in {\mathbb R}^n\) ; in short: We solve the linear equation system \(A x = b\) . Formally, the solution is obtained by \(x = A^{-1} b\) .

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LR-Decomposition of a Matrix

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  • 发表日期：

    2026年

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  • Christian Karpfinger

摘要

We consider the problem of determining a vector \(x \in {\mathbb R}^{n\times n}\) with \(A \, x = b\) for an invertible matrix \(A \in {\mathbb R}^{n\times n}\) and a vector \(b \in {\mathbb R}^n\) ; in short: We solve the linear equation system \(A x = b\) . Formally, the solution is obtained by \(x = A^{-1} b\) .